📢 Too many exams? Don’t know which one suits you best? Book Your Free Expert 👉 call Now!

    Question

    In ∆ABC , G is the centroid , AB = 8 cm, BC= 10 cm and

    AC = 12 cm , find GD, where D is the mid-point of BC?
    A √94/3 cm Correct Answer Incorrect Answer
    B 2√79/3 cm Correct Answer Incorrect Answer
    C √79/3 cm Correct Answer Incorrect Answer
    D 6√13/3 cm Correct Answer Incorrect Answer

    Solution

    If AD is the median, then we know, AB² + AC² = 2{AD² + (BC/2)²} or 82 +  122  = 2{AD 2 + (10/2) 2 } or 64 + 144 = 2{AD 2 + 25} or 208/2 =  AD 2  + 25 or 104 = AD 2  + 25 or  AD 2  = 104 – 25 = 79  or AD = √79 = √79 Now G divides median in 2:1 so GD = 1/3 of AD = 1/3 of 4√13 = 4√13/3cm

    Practice Next
    More Geometry Questions
    ask-question